Small birhombatodecachoron

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Small birhombatodecachoron
Rank4
TypeIsogonal
Notation
Bowers style acronymSabred
Coxeter diagramao3ob3bo3oa&#zc (1/2 < b:a < 3)
Elements
Cells30 tetragonal disphenoids, 10 octahedra, 20 triangular antiprisms, 40 triangular antipodiums
Faces20+40+40 triangles, 120+120 isosceles triangles
Edges60+120+120
Vertices60
Vertex figureApex-truncated augmented triangular prism
Measures (based on two small rhombated pentachora of edge length 1)
Edge lengthsLacing edges (120):
 Base edge 1 (60): 1
 Base edge 2 (120): 1
Circumradius
Central density1
Related polytopes
ArmySabred
RegimentSabred
DualSmall biorthodecachoron
Abstract & topological properties
Flag count4080
Euler characteristic0
OrientableYes
Properties
SymmetryA4×2, order 240
ConvexYes
NatureTame

The small birhombatodecachoron or sabred is a convex isogonal polychoron that consists of 10 octahedra, 20 triangular antiprisms, 40 triangular antipodiums, and 30 tetragonal disphenoids. 1 octahedron, 2 triangular antiprisms, 4 triangular antipodiums, and 2 tetragonal disphenoids join at each vertex.

It is one of a total of five distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite small rhombated pentachora. In this case, the ratio between the edges of the small rhombated pentachoron a3o3b3o is between b:a = 1/2 (producing the rectified small prismatodecachoron) and b:a = 3 (producing the rectified decachoron). This includes the convex hull of two uniform small rhombated pentachora. The lacing edges generally have length .

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.29099.

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